LMFDB - Embedded newform 3525.2.a.bg.1.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3525,2,Mod(1,3525)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3525, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("3525.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3525 = 3 \cdot 5^{2} \cdot 47 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3525.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$28.1472667125$
Analytic rank:	$1$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 3x^{9} - 9x^{8} + 29x^{7} + 25x^{6} - 91x^{5} - 21x^{4} + 101x^{3} + 6x^{2} - 30x - 4 $ x^10 - 3x^9 - 9x^8 + 29x^7 + 25x^6 - 91x^5 - 21x^4 + 101x^3 + 6x^2 - 30*x - 4
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 705)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Root			$1.55802$ of defining polynomial
Character	$\chi$	$=$	3525.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.55802 q^{2} -1.00000 q^{3} +0.427425 q^{4} -1.55802 q^{6} +3.87455 q^{7} -2.45010 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.55802 q^{2} -1.00000 q^{3} +0.427425 q^{4} -1.55802 q^{6} +3.87455 q^{7} -2.45010 q^{8} +1.00000 q^{9} +1.67382 q^{11} -0.427425 q^{12} -2.12123 q^{13} +6.03662 q^{14} -4.67216 q^{16} -5.31859 q^{17} +1.55802 q^{18} -8.33742 q^{19} -3.87455 q^{21} +2.60785 q^{22} +0.669466 q^{23} +2.45010 q^{24} -3.30492 q^{26} -1.00000 q^{27} +1.65608 q^{28} +3.15855 q^{29} -2.86625 q^{31} -2.37911 q^{32} -1.67382 q^{33} -8.28647 q^{34} +0.427425 q^{36} +0.398041 q^{37} -12.9899 q^{38} +2.12123 q^{39} -11.3299 q^{41} -6.03662 q^{42} +1.82268 q^{43} +0.715434 q^{44} +1.04304 q^{46} +1.00000 q^{47} +4.67216 q^{48} +8.01211 q^{49} +5.31859 q^{51} -0.906669 q^{52} -2.61130 q^{53} -1.55802 q^{54} -9.49303 q^{56} +8.33742 q^{57} +4.92108 q^{58} -2.45585 q^{59} +12.4426 q^{61} -4.46567 q^{62} +3.87455 q^{63} +5.63762 q^{64} -2.60785 q^{66} +0.720799 q^{67} -2.27330 q^{68} -0.669466 q^{69} +8.17608 q^{71} -2.45010 q^{72} -14.1727 q^{73} +0.620156 q^{74} -3.56362 q^{76} +6.48530 q^{77} +3.30492 q^{78} -15.8007 q^{79} +1.00000 q^{81} -17.6522 q^{82} -5.57490 q^{83} -1.65608 q^{84} +2.83977 q^{86} -3.15855 q^{87} -4.10104 q^{88} -3.73868 q^{89} -8.21881 q^{91} +0.286147 q^{92} +2.86625 q^{93} +1.55802 q^{94} +2.37911 q^{96} -13.6442 q^{97} +12.4830 q^{98} +1.67382 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 3 q^{2} - 10 q^{3} + 7 q^{4} - 3 q^{6} + 9 q^{8} + 10 q^{9}+O(q^{10}) $ 10 * q + 3 * q^2 - 10 * q^3 + 7 * q^4 - 3 * q^6 + 9 * q^8 + 10 * q^9	$ 10 q + 3 q^{2} - 10 q^{3} + 7 q^{4} - 3 q^{6} + 9 q^{8} + 10 q^{9} - 16 q^{11} - 7 q^{12} + q^{13} - 12 q^{14} - 3 q^{16} + 14 q^{17} + 3 q^{18} - 26 q^{19} + 7 q^{23} - 9 q^{24} - 10 q^{26} - 10 q^{27} - 24 q^{28} - 14 q^{29} - 22 q^{31} + 11 q^{32} + 16 q^{33} - 12 q^{34} + 7 q^{36} + 2 q^{37} - 2 q^{38} - q^{39} - 22 q^{41} + 12 q^{42} - 11 q^{43} - 36 q^{44} - 14 q^{46} + 10 q^{47} + 3 q^{48} + 2 q^{49} - 14 q^{51} + 14 q^{52} + 22 q^{53} - 3 q^{54} - 48 q^{56} + 26 q^{57} - 20 q^{58} - 37 q^{59} - 25 q^{61} - 2 q^{62} - 7 q^{64} - 4 q^{67} + 8 q^{68} - 7 q^{69} - 27 q^{71} + 9 q^{72} + q^{73} + 4 q^{74} - 42 q^{76} + 34 q^{77} + 10 q^{78} + 5 q^{79} + 10 q^{81} - 32 q^{82} + 2 q^{83} + 24 q^{84} - 6 q^{86} + 14 q^{87} - 58 q^{88} + 9 q^{89} - 64 q^{91} + 34 q^{92} + 22 q^{93} + 3 q^{94} - 11 q^{96} - 40 q^{97} + 29 q^{98} - 16 q^{99}+O(q^{100}) $ 10 * q + 3 * q^2 - 10 * q^3 + 7 * q^4 - 3 * q^6 + 9 * q^8 + 10 * q^9 - 16 * q^11 - 7 * q^12 + q^13 - 12 * q^14 - 3 * q^16 + 14 * q^17 + 3 * q^18 - 26 * q^19 + 7 * q^23 - 9 * q^24 - 10 * q^26 - 10 * q^27 - 24 * q^28 - 14 * q^29 - 22 * q^31 + 11 * q^32 + 16 * q^33 - 12 * q^34 + 7 * q^36 + 2 * q^37 - 2 * q^38 - q^39 - 22 * q^41 + 12 * q^42 - 11 * q^43 - 36 * q^44 - 14 * q^46 + 10 * q^47 + 3 * q^48 + 2 * q^49 - 14 * q^51 + 14 * q^52 + 22 * q^53 - 3 * q^54 - 48 * q^56 + 26 * q^57 - 20 * q^58 - 37 * q^59 - 25 * q^61 - 2 * q^62 - 7 * q^64 - 4 * q^67 + 8 * q^68 - 7 * q^69 - 27 * q^71 + 9 * q^72 + q^73 + 4 * q^74 - 42 * q^76 + 34 * q^77 + 10 * q^78 + 5 * q^79 + 10 * q^81 - 32 * q^82 + 2 * q^83 + 24 * q^84 - 6 * q^86 + 14 * q^87 - 58 * q^88 + 9 * q^89 - 64 * q^91 + 34 * q^92 + 22 * q^93 + 3 * q^94 - 11 * q^96 - 40 * q^97 + 29 * q^98 - 16 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	1.55802	1.10169	0.550843	−	0.834609i	$-0.314306\pi$
$2$	1.55802	1.10169	0.550843	+	0.834609i	$0.314306\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	0.427425	0.213713
$5$	0	0
$5$	0	0
$6$	−1.55802	−0.636059
$7$	3.87455	1.46444	0.732220	−	0.681068i	$-0.238484\pi$
$7$	3.87455	1.46444	0.732220	+	0.681068i	$0.238484\pi$
$8$	−2.45010	−0.866242
$9$	1.00000	0.333333
$10$	0	0
$11$	1.67382	0.504676	0.252338	−	0.967639i	$-0.418800\pi$
$11$	1.67382	0.504676	0.252338	+	0.967639i	$0.418800\pi$
$12$	−0.427425	−0.123387
$13$	−2.12123	−0.588324	−0.294162	−	0.955756i	$-0.595041\pi$
$13$	−2.12123	−0.588324	−0.294162	+	0.955756i	$0.595041\pi$
$14$	6.03662	1.61335
$15$	0	0
$16$	−4.67216	−1.16804
$17$	−5.31859	−1.28995	−0.644974	−	0.764204i	$-0.723132\pi$
$17$	−5.31859	−1.28995	−0.644974	+	0.764204i	$0.723132\pi$
$18$	1.55802	0.367229
$19$	−8.33742	−1.91273	−0.956367	−	0.292167i	$-0.905624\pi$
$19$	−8.33742	−1.91273	−0.956367	+	0.292167i	$0.905624\pi$
$20$	0	0
$21$	−3.87455	−0.845495
$22$	2.60785	0.555995
$23$	0.669466	0.139593	0.0697967	−	0.997561i	$-0.477765\pi$
$23$	0.669466	0.139593	0.0697967	+	0.997561i	$0.477765\pi$
$24$	2.45010	0.500125
$25$	0	0
$26$	−3.30492	−0.648149
$27$	−1.00000	−0.192450
$28$	1.65608	0.312970
$29$	3.15855	0.586528	0.293264	−	0.956032i	$-0.405259\pi$
$29$	3.15855	0.586528	0.293264	+	0.956032i	$0.405259\pi$
$30$	0	0
$31$	−2.86625	−0.514793	−0.257397	−	0.966306i	$-0.582865\pi$
$31$	−2.86625	−0.514793	−0.257397	+	0.966306i	$0.582865\pi$
$32$	−2.37911	−0.420571
$33$	−1.67382	−0.291375
$34$	−8.28647	−1.42112
$35$	0	0
$36$	0.427425	0.0712376
$37$	0.398041	0.0654376	0.0327188	−	0.999465i	$-0.489583\pi$
$37$	0.398041	0.0654376	0.0327188	+	0.999465i	$0.489583\pi$
$38$	−12.9899	−2.10723
$39$	2.12123	0.339669
$40$	0	0
$41$	−11.3299	−1.76943	−0.884714	−	0.466133i	$-0.845647\pi$
$41$	−11.3299	−1.76943	−0.884714	+	0.466133i	$0.845647\pi$
$42$	−6.03662	−0.931470
$43$	1.82268	0.277956	0.138978	−	0.990295i	$-0.455618\pi$
$43$	1.82268	0.277956	0.138978	+	0.990295i	$0.455618\pi$
$44$	0.715434	0.107856
$45$	0	0
$46$	1.04304	0.153788
$47$	1.00000	0.145865
$47$	1.00000	0.145865
$48$	4.67216	0.674368
$49$	8.01211	1.14459
$50$	0	0
$51$	5.31859	0.744752
$52$	−0.906669	−0.125732
$53$	−2.61130	−0.358690	−0.179345	−	0.983786i	$-0.557398\pi$
$53$	−2.61130	−0.358690	−0.179345	+	0.983786i	$0.557398\pi$
$54$	−1.55802	−0.212020
$55$	0	0
$56$	−9.49303	−1.26856
$57$	8.33742	1.10432
$58$	4.92108	0.646170
$59$	−2.45585	−0.319724	−0.159862	−	0.987139i	$-0.551105\pi$
$59$	−2.45585	−0.319724	−0.159862	+	0.987139i	$0.551105\pi$
$60$	0	0
$61$	12.4426	1.59311	0.796555	−	0.604566i	$-0.206653\pi$
$61$	12.4426	1.59311	0.796555	+	0.604566i	$0.206653\pi$
$62$	−4.46567	−0.567141
$63$	3.87455	0.488147
$64$	5.63762	0.704702
$65$	0	0
$66$	−2.60785	−0.321004
$67$	0.720799	0.0880596	0.0440298	−	0.999030i	$-0.485980\pi$
$67$	0.720799	0.0880596	0.0440298	+	0.999030i	$0.485980\pi$
$68$	−2.27330	−0.275678
$69$	−0.669466	−0.0805943
$70$	0	0
$71$	8.17608	0.970322	0.485161	−	0.874425i	$-0.338761\pi$
$71$	8.17608	0.970322	0.485161	+	0.874425i	$0.338761\pi$
$72$	−2.45010	−0.288747
$73$	−14.1727	−1.65879	−0.829397	−	0.558659i	$-0.811316\pi$
$73$	−14.1727	−1.65879	−0.829397	+	0.558659i	$0.811316\pi$
$74$	0.620156	0.0720917
$75$	0	0
$76$	−3.56362	−0.408776
$77$	6.48530	0.739069
$78$	3.30492	0.374209
$79$	−15.8007	−1.77772	−0.888861	−	0.458177i	$-0.848502\pi$
$79$	−15.8007	−1.77772	−0.888861	+	0.458177i	$0.848502\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	−17.6522	−1.94936
$83$	−5.57490	−0.611925	−0.305962	−	0.952044i	$-0.598978\pi$
$83$	−5.57490	−0.611925	−0.305962	+	0.952044i	$0.598978\pi$
$84$	−1.65608	−0.180693
$85$	0	0
$86$	2.83977	0.306220
$87$	−3.15855	−0.338632
$88$	−4.10104	−0.437172
$89$	−3.73868	−0.396299	−0.198150	−	0.980172i	$-0.563493\pi$
$89$	−3.73868	−0.396299	−0.198150	+	0.980172i	$0.563493\pi$
$90$	0	0
$91$	−8.21881	−0.861566
$92$	0.286147	0.0298329
$93$	2.86625	0.297216
$94$	1.55802	0.160697
$95$	0	0
$96$	2.37911	0.242817
$97$	−13.6442	−1.38536	−0.692680	−	0.721245i	$-0.743570\pi$
$97$	−13.6442	−1.38536	−0.692680	+	0.721245i	$0.743570\pi$
$98$	12.4830	1.26098
$99$	1.67382	0.168225
$100$	0	0
$101$	−4.56073	−0.453810	−0.226905	−	0.973917i	$-0.572861\pi$
$101$	−4.56073	−0.453810	−0.226905	+	0.973917i	$0.572861\pi$
$102$	8.28647	0.820483
$103$	−4.91561	−0.484349	−0.242175	−	0.970233i	$-0.577861\pi$
$103$	−4.91561	−0.484349	−0.242175	+	0.970233i	$0.577861\pi$
$104$	5.19724	0.509631
$105$	0	0
$106$	−4.06846	−0.395164
$107$	−2.44138	−0.236017	−0.118009	−	0.993013i	$-0.537651\pi$
$107$	−2.44138	−0.236017	−0.118009	+	0.993013i	$0.537651\pi$
$108$	−0.427425	−0.0411290
$109$	−8.26373	−0.791522	−0.395761	−	0.918354i	$-0.629519\pi$
$109$	−8.26373	−0.791522	−0.395761	+	0.918354i	$0.629519\pi$
$110$	0	0
$111$	−0.398041	−0.0377804
$112$	−18.1025	−1.71052
$113$	16.8631	1.58635	0.793175	−	0.608994i	$-0.208427\pi$
$113$	16.8631	1.58635	0.793175	+	0.608994i	$0.208427\pi$
$114$	12.9899	1.21661
$115$	0	0
$116$	1.35004	0.125348
$117$	−2.12123	−0.196108
$118$	−3.82626	−0.352235
$119$	−20.6071	−1.88905
$120$	0	0
$121$	−8.19832	−0.745302
$122$	19.3858	1.75511
$123$	11.3299	1.02158
$124$	−1.22511	−0.110018
$125$	0	0
$126$	6.03662	0.537785
$127$	19.2540	1.70851	0.854257	−	0.519850i	$-0.174012\pi$
$127$	19.2540	1.70851	0.854257	+	0.519850i	$0.174012\pi$
$128$	13.5417	1.19693
$129$	−1.82268	−0.160478
$130$	0	0
$131$	−7.72157	−0.674637	−0.337318	−	0.941391i	$-0.609520\pi$
$131$	−7.72157	−0.674637	−0.337318	+	0.941391i	$0.609520\pi$
$132$	−0.715434	−0.0622705
$133$	−32.3037	−2.80109
$134$	1.12302	0.0970140
$135$	0	0
$136$	13.0311	1.11741
$137$	19.9662	1.70583	0.852913	−	0.522053i	$-0.174834\pi$
$137$	19.9662	1.70583	0.852913	+	0.522053i	$0.174834\pi$
$138$	−1.04304	−0.0887896
$139$	2.90594	0.246479	0.123239	−	0.992377i	$-0.460672\pi$
$139$	2.90594	0.246479	0.123239	+	0.992377i	$0.460672\pi$
$140$	0	0
$141$	−1.00000	−0.0842152
$142$	12.7385	1.06899
$143$	−3.55057	−0.296913
$144$	−4.67216	−0.389347
$145$	0	0
$146$	−22.0814	−1.82747
$147$	−8.01211	−0.660827
$148$	0.170133	0.0139848
$149$	−12.7231	−1.04232	−0.521158	−	0.853460i	$-0.674500\pi$
$149$	−12.7231	−1.04232	−0.521158	+	0.853460i	$0.674500\pi$
$150$	0	0
$151$	−19.0537	−1.55057	−0.775286	−	0.631611i	$-0.782394\pi$
$151$	−19.0537	−1.55057	−0.775286	+	0.631611i	$0.782394\pi$
$152$	20.4275	1.65689
$153$	−5.31859	−0.429983
$154$	10.1042	0.814222
$155$	0	0
$156$	0.906669	0.0725916
$157$	−7.84774	−0.626318	−0.313159	−	0.949701i	$-0.601387\pi$
$157$	−7.84774	−0.626318	−0.313159	+	0.949701i	$0.601387\pi$
$158$	−24.6179	−1.95849
$159$	2.61130	0.207090
$160$	0	0
$161$	2.59388	0.204426
$162$	1.55802	0.122410
$163$	23.9243	1.87389	0.936946	−	0.349474i	$-0.113640\pi$
$163$	23.9243	1.87389	0.936946	+	0.349474i	$0.113640\pi$
$164$	−4.84268	−0.378149
$165$	0	0
$166$	−8.68580	−0.674149
$167$	7.87294	0.609226	0.304613	−	0.952476i	$-0.401473\pi$
$167$	7.87294	0.609226	0.304613	+	0.952476i	$0.401473\pi$
$168$	9.49303	0.732403
$169$	−8.50037	−0.653875
$170$	0	0
$171$	−8.33742	−0.637578
$172$	0.779059	0.0594027
$173$	−21.5863	−1.64118	−0.820589	−	0.571518i	$-0.806355\pi$
$173$	−21.5863	−1.64118	−0.820589	+	0.571518i	$0.806355\pi$
$174$	−4.92108	−0.373066
$175$	0	0
$176$	−7.82036	−0.589482
$177$	2.45585	0.184593
$178$	−5.82494	−0.436597
$179$	−6.16737	−0.460971	−0.230486	−	0.973076i	$-0.574031\pi$
$179$	−6.16737	−0.460971	−0.230486	+	0.973076i	$0.574031\pi$
$180$	0	0
$181$	−20.4173	−1.51761	−0.758805	−	0.651318i	$-0.774216\pi$
$181$	−20.4173	−1.51761	−0.758805	+	0.651318i	$0.774216\pi$
$182$	−12.8051	−0.949175
$183$	−12.4426	−0.919783
$184$	−1.64026	−0.120922
$185$	0	0
$186$	4.46567	0.327439
$187$	−8.90238	−0.651006
$188$	0.427425	0.0311732
$189$	−3.87455	−0.281832
$190$	0	0
$191$	7.84659	0.567759	0.283880	−	0.958860i	$-0.408378\pi$
$191$	7.84659	0.567759	0.283880	+	0.958860i	$0.408378\pi$
$192$	−5.63762	−0.406860
$193$	−11.2626	−0.810700	−0.405350	−	0.914161i	$-0.632850\pi$
$193$	−11.2626	−0.810700	−0.405350	+	0.914161i	$0.632850\pi$
$194$	−21.2579	−1.52623
$195$	0	0
$196$	3.42458	0.244613
$197$	−5.49967	−0.391835	−0.195918	−	0.980620i	$-0.562769\pi$
$197$	−5.49967	−0.391835	−0.195918	+	0.980620i	$0.562769\pi$
$198$	2.60785	0.185332
$199$	14.9707	1.06125	0.530623	−	0.847608i	$-0.321958\pi$
$199$	14.9707	1.06125	0.530623	+	0.847608i	$0.321958\pi$
$200$	0	0
$201$	−0.720799	−0.0508412
$202$	−7.10571	−0.499956
$203$	12.2379	0.858935
$204$	2.27330	0.159163
$205$	0	0
$206$	−7.65862	−0.533601
$207$	0.669466	0.0465311
$208$	9.91073	0.687186
$209$	−13.9554	−0.965312
$210$	0	0
$211$	−2.58347	−0.177853	−0.0889267	−	0.996038i	$-0.528344\pi$
$211$	−2.58347	−0.177853	−0.0889267	+	0.996038i	$0.528344\pi$
$212$	−1.11614	−0.0766567
$213$	−8.17608	−0.560216
$214$	−3.80372	−0.260017
$215$	0	0
$216$	2.45010	0.166708
$217$	−11.1054	−0.753884
$218$	−12.8751	−0.872009
$219$	14.1727	0.957705
$220$	0	0
$221$	11.2820	0.758907
$222$	−0.620156	−0.0416222
$223$	0.956824	0.0640737	0.0320368	−	0.999487i	$-0.489801\pi$
$223$	0.956824	0.0640737	0.0320368	+	0.999487i	$0.489801\pi$
$224$	−9.21797	−0.615902
$225$	0	0
$226$	26.2731	1.74766
$227$	2.45535	0.162967	0.0814836	−	0.996675i	$-0.474034\pi$
$227$	2.45535	0.162967	0.0814836	+	0.996675i	$0.474034\pi$
$228$	3.56362	0.236007
$229$	−4.34066	−0.286839	−0.143419	−	0.989662i	$-0.545810\pi$
$229$	−4.34066	−0.286839	−0.143419	+	0.989662i	$0.545810\pi$
$230$	0	0
$231$	−6.48530	−0.426701
$232$	−7.73877	−0.508075
$233$	5.97881	0.391685	0.195843	−	0.980635i	$-0.437256\pi$
$233$	5.97881	0.391685	0.195843	+	0.980635i	$0.437256\pi$
$234$	−3.30492	−0.216050
$235$	0	0
$236$	−1.04969	−0.0683290
$237$	15.8007	1.02637
$238$	−32.1063	−2.08114
$239$	−22.8096	−1.47543	−0.737716	−	0.675111i	$-0.764096\pi$
$239$	−22.8096	−1.47543	−0.737716	+	0.675111i	$0.764096\pi$
$240$	0	0
$241$	5.79509	0.373295	0.186647	−	0.982427i	$-0.440238\pi$
$241$	5.79509	0.373295	0.186647	+	0.982427i	$0.440238\pi$
$242$	−12.7731	−0.821089
$243$	−1.00000	−0.0641500
$244$	5.31828	0.340468
$245$	0	0
$246$	17.6522	1.12546
$247$	17.6856	1.12531
$248$	7.02260	0.445935
$249$	5.57490	0.353295
$250$	0	0
$251$	−12.4869	−0.788164	−0.394082	−	0.919075i	$-0.628937\pi$
$251$	−12.4869	−0.788164	−0.394082	+	0.919075i	$0.628937\pi$
$252$	1.65608	0.104323
$253$	1.12057	0.0704495
$254$	29.9981	1.88225
$255$	0	0
$256$	9.82306	0.613941
$257$	16.0155	0.999019	0.499509	−	0.866309i	$-0.333514\pi$
$257$	16.0155	0.999019	0.499509	+	0.866309i	$0.333514\pi$
$258$	−2.83977	−0.176796
$259$	1.54223	0.0958294
$260$	0	0
$261$	3.15855	0.195509
$262$	−12.0304	−0.743238
$263$	5.41400	0.333841	0.166921	−	0.985970i	$-0.446618\pi$
$263$	5.41400	0.333841	0.166921	+	0.985970i	$0.446618\pi$
$264$	4.10104	0.252401
$265$	0	0
$266$	−50.3298	−3.08592
$267$	3.73868	0.228803
$268$	0.308088	0.0188195
$269$	29.6868	1.81004	0.905018	−	0.425372i	$-0.139857\pi$
$269$	29.6868	1.81004	0.905018	+	0.425372i	$0.139857\pi$
$270$	0	0
$271$	−4.27710	−0.259815	−0.129908	−	0.991526i	$-0.541468\pi$
$271$	−4.27710	−0.259815	−0.129908	+	0.991526i	$0.541468\pi$
$272$	24.8493	1.50671
$273$	8.21881	0.497425
$274$	31.1077	1.87928
$275$	0	0
$276$	−0.286147	−0.0172240
$277$	−10.0695	−0.605019	−0.302510	−	0.953146i	$-0.597824\pi$
$277$	−10.0695	−0.605019	−0.302510	+	0.953146i	$0.597824\pi$
$278$	4.52752	0.271542
$279$	−2.86625	−0.171598
$280$	0	0
$281$	18.4511	1.10070	0.550351	−	0.834933i	$-0.314494\pi$
$281$	18.4511	1.10070	0.550351	+	0.834933i	$0.314494\pi$
$282$	−1.55802	−0.0927787
$283$	16.4247	0.976349	0.488174	−	0.872746i	$-0.337663\pi$
$283$	16.4247	0.976349	0.488174	+	0.872746i	$0.337663\pi$
$284$	3.49466	0.207370
$285$	0	0
$286$	−5.53185	−0.327105
$287$	−43.8981	−2.59122
$288$	−2.37911	−0.140190
$289$	11.2874	0.663966
$290$	0	0
$291$	13.6442	0.799838
$292$	−6.05779	−0.354505
$293$	25.6582	1.49897	0.749483	−	0.662023i	$-0.230302\pi$
$293$	25.6582	1.49897	0.749483	+	0.662023i	$0.230302\pi$
$294$	−12.4830	−0.728024
$295$	0	0
$296$	−0.975242	−0.0566848
$297$	−1.67382	−0.0971250
$298$	−19.8228	−1.14831
$299$	−1.42009	−0.0821261
$300$	0	0
$301$	7.06205	0.407050
$302$	−29.6861	−1.70824
$303$	4.56073	0.262007
$304$	38.9537	2.23415
$305$	0	0
$306$	−8.28647	−0.473706
$307$	7.82693	0.446707	0.223353	−	0.974738i	$-0.428300\pi$
$307$	7.82693	0.446707	0.223353	+	0.974738i	$0.428300\pi$
$308$	2.77198	0.157948
$309$	4.91561	0.279639
$310$	0	0
$311$	−1.69175	−0.0959304	−0.0479652	−	0.998849i	$-0.515274\pi$
$311$	−1.69175	−0.0959304	−0.0479652	+	0.998849i	$0.515274\pi$
$312$	−5.19724	−0.294236
$313$	−5.43076	−0.306965	−0.153482	−	0.988151i	$-0.549049\pi$
$313$	−5.43076	−0.306965	−0.153482	+	0.988151i	$0.549049\pi$
$314$	−12.2269	−0.690006
$315$	0	0
$316$	−6.75364	−0.379922
$317$	5.09510	0.286169	0.143085	−	0.989710i	$-0.454298\pi$
$317$	5.09510	0.286169	0.143085	+	0.989710i	$0.454298\pi$
$318$	4.06846	0.228148
$319$	5.28685	0.296007
$320$	0	0
$321$	2.44138	0.136265
$322$	4.04131	0.225214
$323$	44.3433	2.46733
$324$	0.427425	0.0237459
$325$	0	0
$326$	37.2745	2.06444
$327$	8.26373	0.456985
$328$	27.7593	1.53275
$329$	3.87455	0.213611
$330$	0	0
$331$	−8.65332	−0.475629	−0.237815	−	0.971311i	$-0.576431\pi$
$331$	−8.65332	−0.475629	−0.237815	+	0.971311i	$0.576431\pi$
$332$	−2.38285	−0.130776
$333$	0.398041	0.0218125
$334$	12.2662	0.671176
$335$	0	0
$336$	18.1025	0.987572
$337$	23.9207	1.30304	0.651521	−	0.758631i	$-0.274131\pi$
$337$	23.9207	1.30304	0.651521	+	0.758631i	$0.274131\pi$
$338$	−13.2437	−0.720365
$339$	−16.8631	−0.915879
$340$	0	0
$341$	−4.79759	−0.259804
$342$	−12.9899	−0.702411
$343$	3.92145	0.211738
$344$	−4.46575	−0.240777
$345$	0	0
$346$	−33.6319	−1.80806
$347$	3.91600	0.210222	0.105111	−	0.994461i	$-0.466480\pi$
$347$	3.91600	0.210222	0.105111	+	0.994461i	$0.466480\pi$
$348$	−1.35004	−0.0723700
$349$	−25.6427	−1.37262	−0.686310	−	0.727309i	$-0.740771\pi$
$349$	−25.6427	−1.37262	−0.686310	+	0.727309i	$0.740771\pi$
$350$	0	0
$351$	2.12123	0.113223
$352$	−3.98221	−0.212252
$353$	10.3163	0.549081	0.274540	−	0.961576i	$-0.411474\pi$
$353$	10.3163	0.549081	0.274540	+	0.961576i	$0.411474\pi$
$354$	3.82626	0.203363
$355$	0	0
$356$	−1.59801	−0.0846942
$357$	20.6071	1.09064
$358$	−9.60889	−0.507845
$359$	−35.3075	−1.86346	−0.931730	−	0.363152i	$-0.881701\pi$
$359$	−35.3075	−1.86346	−0.931730	+	0.363152i	$0.881701\pi$
$360$	0	0
$361$	50.5125	2.65855
$362$	−31.8106	−1.67193
$363$	8.19832	0.430300
$364$	−3.51293	−0.184128
$365$	0	0
$366$	−19.3858	−1.01331
$367$	−31.0761	−1.62216	−0.811081	−	0.584934i	$-0.801120\pi$
$367$	−31.0761	−1.62216	−0.811081	+	0.584934i	$0.801120\pi$
$368$	−3.12785	−0.163051
$369$	−11.3299	−0.589810
$370$	0	0
$371$	−10.1176	−0.525281
$372$	1.22511	0.0635188
$373$	12.2252	0.632998	0.316499	−	0.948593i	$-0.397493\pi$
$373$	12.2252	0.632998	0.316499	+	0.948593i	$0.397493\pi$
$374$	−13.8701	−0.717205
$375$	0	0
$376$	−2.45010	−0.126354
$377$	−6.70002	−0.345069
$378$	−6.03662	−0.310490
$379$	13.7419	0.705873	0.352936	−	0.935647i	$-0.385183\pi$
$379$	13.7419	0.705873	0.352936	+	0.935647i	$0.385183\pi$
$380$	0	0
$381$	−19.2540	−0.986411
$382$	12.2251	0.625493
$383$	31.2761	1.59813	0.799067	−	0.601242i	$-0.205327\pi$
$383$	31.2761	1.59813	0.799067	+	0.601242i	$0.205327\pi$
$384$	−13.5417	−0.691049
$385$	0	0
$386$	−17.5474	−0.893138
$387$	1.82268	0.0926519
$388$	−5.83188	−0.296069
$389$	−28.1852	−1.42905	−0.714524	−	0.699611i	$-0.753357\pi$
$389$	−28.1852	−1.42905	−0.714524	+	0.699611i	$0.753357\pi$
$390$	0	0
$391$	−3.56062	−0.180068
$392$	−19.6305	−0.991489
$393$	7.72157	0.389502
$394$	−8.56859	−0.431679
$395$	0	0
$396$	0.715434	0.0359519
$397$	7.43456	0.373130	0.186565	−	0.982443i	$-0.440264\pi$
$397$	7.43456	0.373130	0.186565	+	0.982443i	$0.440264\pi$
$398$	23.3247	1.16916
$399$	32.3037	1.61721
$400$	0	0
$401$	−11.6308	−0.580815	−0.290408	−	0.956903i	$-0.593791\pi$
$401$	−11.6308	−0.580815	−0.290408	+	0.956903i	$0.593791\pi$
$402$	−1.12302	−0.0560111
$403$	6.07998	0.302865
$404$	−1.94937	−0.0969849
$405$	0	0
$406$	19.0670	0.946277
$407$	0.666250	0.0330248
$408$	−13.0311	−0.645135
$409$	−18.8108	−0.930135	−0.465067	−	0.885275i	$-0.653970\pi$
$409$	−18.8108	−0.930135	−0.465067	+	0.885275i	$0.653970\pi$
$410$	0	0
$411$	−19.9662	−0.984859
$412$	−2.10106	−0.103512
$413$	−9.51529	−0.468217
$414$	1.04304	0.0512627
$415$	0	0
$416$	5.04665	0.247432
$417$	−2.90594	−0.142305
$418$	−21.7427	−1.06347
$419$	5.76522	0.281650	0.140825	−	0.990035i	$-0.455025\pi$
$419$	5.76522	0.281650	0.140825	+	0.990035i	$0.455025\pi$
$420$	0	0
$421$	−8.44411	−0.411541	−0.205770	−	0.978600i	$-0.565970\pi$
$421$	−8.44411	−0.411541	−0.205770	+	0.978600i	$0.565970\pi$
$422$	−4.02510	−0.195939
$423$	1.00000	0.0486217
$424$	6.39796	0.310713
$425$	0	0
$426$	−12.7385	−0.617182
$427$	48.2094	2.33302
$428$	−1.04351	−0.0504398
$429$	3.55057	0.171423
$430$	0	0
$431$	22.0375	1.06151	0.530754	−	0.847526i	$-0.321909\pi$
$431$	22.0375	1.06151	0.530754	+	0.847526i	$0.321909\pi$
$432$	4.67216	0.224789
$433$	35.5013	1.70608	0.853041	−	0.521843i	$-0.174755\pi$
$433$	35.5013	1.70608	0.853041	+	0.521843i	$0.174755\pi$
$434$	−17.3024	−0.830544
$435$	0	0
$436$	−3.53213	−0.169158
$437$	−5.58162	−0.267005
$438$	22.0814	1.05509
$439$	32.1001	1.53205	0.766027	−	0.642808i	$-0.222231\pi$
$439$	32.1001	1.53205	0.766027	+	0.642808i	$0.222231\pi$
$440$	0	0
$441$	8.01211	0.381529
$442$	17.5775	0.836078
$443$	−12.9184	−0.613773	−0.306886	−	0.951746i	$-0.599287\pi$
$443$	−12.9184	−0.613773	−0.306886	+	0.951746i	$0.599287\pi$
$444$	−0.170133	−0.00807415
$445$	0	0
$446$	1.49075	0.0705891
$447$	12.7231	0.601782
$448$	21.8432	1.03199
$449$	16.8553	0.795451	0.397726	−	0.917504i	$-0.369800\pi$
$449$	16.8553	0.795451	0.397726	+	0.917504i	$0.369800\pi$
$450$	0	0
$451$	−18.9642	−0.892989
$452$	7.20773	0.339023
$453$	19.0537	0.895223
$454$	3.82548	0.179539
$455$	0	0
$456$	−20.4275	−0.956606
$457$	−11.6787	−0.546304	−0.273152	−	0.961971i	$-0.588066\pi$
$457$	−11.6787	−0.546304	−0.273152	+	0.961971i	$0.588066\pi$
$458$	−6.76283	−0.316006
$459$	5.31859	0.248251
$460$	0	0
$461$	14.0864	0.656067	0.328034	−	0.944666i	$-0.393614\pi$
$461$	14.0864	0.656067	0.328034	+	0.944666i	$0.393614\pi$
$462$	−10.1042	−0.470091
$463$	−7.13177	−0.331442	−0.165721	−	0.986173i	$-0.552995\pi$
$463$	−7.13177	−0.331442	−0.165721	+	0.986173i	$0.552995\pi$
$464$	−14.7572	−0.685088
$465$	0	0
$466$	9.31511	0.431514
$467$	15.6100	0.722342	0.361171	−	0.932500i	$-0.382377\pi$
$467$	15.6100	0.722342	0.361171	+	0.932500i	$0.382377\pi$
$468$	−0.906669	−0.0419108
$469$	2.79277	0.128958
$470$	0	0
$471$	7.84774	0.361605
$472$	6.01707	0.276958
$473$	3.05084	0.140278
$474$	24.6179	1.13074
$475$	0	0
$476$	−8.80801	−0.403714
$477$	−2.61130	−0.119563
$478$	−35.5379	−1.62546
$479$	1.56644	0.0715725	0.0357863	−	0.999359i	$-0.488606\pi$
$479$	1.56644	0.0715725	0.0357863	+	0.999359i	$0.488606\pi$
$480$	0	0
$481$	−0.844338	−0.0384985
$482$	9.02887	0.411254
$483$	−2.59388	−0.118026
$484$	−3.50417	−0.159280
$485$	0	0
$486$	−1.55802	−0.0706732
$487$	6.76390	0.306501	0.153251	−	0.988187i	$-0.451026\pi$
$487$	6.76390	0.306501	0.153251	+	0.988187i	$0.451026\pi$
$488$	−30.4856	−1.38002
$489$	−23.9243	−1.08189
$490$	0	0
$491$	1.29446	0.0584184	0.0292092	−	0.999573i	$-0.490701\pi$
$491$	1.29446	0.0584184	0.0292092	+	0.999573i	$0.490701\pi$
$492$	4.84268	0.218325
$493$	−16.7990	−0.756591
$494$	27.5545	1.23974
$495$	0	0
$496$	13.3916	0.601299
$497$	31.6786	1.42098
$498$	8.68580	0.389220
$499$	5.35126	0.239556	0.119778	−	0.992801i	$-0.461782\pi$
$499$	5.35126	0.239556	0.119778	+	0.992801i	$0.461782\pi$
$500$	0	0
$501$	−7.87294	−0.351737
$502$	−19.4548	−0.868309
$503$	26.7676	1.19351	0.596754	−	0.802425i	$-0.296457\pi$
$503$	26.7676	1.19351	0.596754	+	0.802425i	$0.296457\pi$
$504$	−9.49303	−0.422853
$505$	0	0
$506$	1.74587	0.0776132
$507$	8.50037	0.377515
$508$	8.22964	0.365131
$509$	16.3687	0.725530	0.362765	−	0.931881i	$-0.381833\pi$
$509$	16.3687	0.725530	0.362765	+	0.931881i	$0.381833\pi$
$510$	0	0
$511$	−54.9130	−2.42921
$512$	−11.7790	−0.520561
$513$	8.33742	0.368106
$514$	24.9524	1.10061
$515$	0	0
$516$	−0.779059	−0.0342962
$517$	1.67382	0.0736146
$518$	2.40282	0.105574
$519$	21.5863	0.947535
$520$	0	0
$521$	33.4809	1.46683	0.733413	−	0.679783i	$-0.237926\pi$
$521$	33.4809	1.46683	0.733413	+	0.679783i	$0.237926\pi$
$522$	4.92108	0.215390
$523$	−28.6007	−1.25062	−0.625311	−	0.780376i	$-0.715028\pi$
$523$	−28.6007	−1.25062	−0.625311	+	0.780376i	$0.715028\pi$
$524$	−3.30040	−0.144178
$525$	0	0
$526$	8.43511	0.367788
$527$	15.2444	0.664056
$528$	7.82036	0.340338
$529$	−22.5518	−0.980514
$530$	0	0
$531$	−2.45585	−0.106575
$532$	−13.8074	−0.598628
$533$	24.0333	1.04100
$534$	5.82494	0.252070
$535$	0	0
$536$	−1.76603	−0.0762809
$537$	6.16737	0.266142
$538$	46.2526	1.99409
$539$	13.4108	0.577646
$540$	0	0
$541$	44.5729	1.91634	0.958168	−	0.286205i	$-0.0923939\pi$
$541$	44.5729	1.91634	0.958168	+	0.286205i	$0.0923939\pi$
$542$	−6.66380	−0.286235
$543$	20.4173	0.876192
$544$	12.6535	0.542515
$545$	0	0
$546$	12.8051	0.548006
$547$	−39.0348	−1.66901	−0.834504	−	0.551002i	$-0.814246\pi$
$547$	−39.0348	−1.66901	−0.834504	+	0.551002i	$0.814246\pi$
$548$	8.53405	0.364557
$549$	12.4426	0.531037
$550$	0	0
$551$	−26.3341	−1.12187
$552$	1.64026	0.0698141
$553$	−61.2207	−2.60337
$554$	−15.6885	−0.666542
$555$	0	0
$556$	1.24207	0.0526757
$557$	5.19235	0.220007	0.110003	−	0.993931i	$-0.464914\pi$
$557$	5.19235	0.220007	0.110003	+	0.993931i	$0.464914\pi$
$558$	−4.46567	−0.189047
$559$	−3.86632	−0.163528
$560$	0	0
$561$	8.90238	0.375859
$562$	28.7472	1.21263
$563$	31.0460	1.30843	0.654217	−	0.756307i	$-0.272998\pi$
$563$	31.0460	1.30843	0.654217	+	0.756307i	$0.272998\pi$
$564$	−0.427425	−0.0179979
$565$	0	0
$566$	25.5901	1.07563
$567$	3.87455	0.162716
$568$	−20.0322	−0.840534
$569$	−34.1611	−1.43211	−0.716055	−	0.698044i	$-0.754054\pi$
$569$	−34.1611	−1.43211	−0.716055	+	0.698044i	$0.754054\pi$
$570$	0	0
$571$	0.457455	0.0191439	0.00957195	−	0.999954i	$-0.496953\pi$
$571$	0.457455	0.0191439	0.00957195	+	0.999954i	$0.496953\pi$
$572$	−1.51760	−0.0634541
$573$	−7.84659	−0.327796
$574$	−68.3941	−2.85472
$575$	0	0
$576$	5.63762	0.234901
$577$	33.5583	1.39705	0.698525	−	0.715586i	$-0.253840\pi$
$577$	33.5583	1.39705	0.698525	+	0.715586i	$0.253840\pi$
$578$	17.5860	0.731482
$579$	11.2626	0.468058
$580$	0	0
$581$	−21.6002	−0.896127
$582$	21.2579	0.881170
$583$	−4.37086	−0.181022
$584$	34.7247	1.43692
$585$	0	0
$586$	39.9759	1.65139
$587$	−32.1260	−1.32598	−0.662990	−	0.748628i	$-0.730713\pi$
$587$	−32.1260	−1.32598	−0.662990	+	0.748628i	$0.730713\pi$
$588$	−3.42458	−0.141227
$589$	23.8971	0.984663
$590$	0	0
$591$	5.49967	0.226226
$592$	−1.85971	−0.0764337
$593$	13.4105	0.550704	0.275352	−	0.961343i	$-0.411206\pi$
$593$	13.4105	0.550704	0.275352	+	0.961343i	$0.411206\pi$
$594$	−2.60785	−0.107001
$595$	0	0
$596$	−5.43817	−0.222756
$597$	−14.9707	−0.612711
$598$	−2.21253	−0.0904772
$599$	20.9045	0.854133	0.427067	−	0.904220i	$-0.359547\pi$
$599$	20.9045	0.854133	0.427067	+	0.904220i	$0.359547\pi$
$600$	0	0
$601$	21.0432	0.858368	0.429184	−	0.903217i	$-0.358801\pi$
$601$	21.0432	0.858368	0.429184	+	0.903217i	$0.358801\pi$
$602$	11.0028	0.448441
$603$	0.720799	0.0293532
$604$	−8.14405	−0.331377
$605$	0	0
$606$	7.10571	0.288650
$607$	−14.3823	−0.583759	−0.291879	−	0.956455i	$-0.594281\pi$
$607$	−14.3823	−0.583759	−0.291879	+	0.956455i	$0.594281\pi$
$608$	19.8356	0.804441
$609$	−12.2379	−0.495907
$610$	0	0
$611$	−2.12123	−0.0858159
$612$	−2.27330	−0.0918928
$613$	−29.5540	−1.19367	−0.596836	−	0.802363i	$-0.703576\pi$
$613$	−29.5540	−1.19367	−0.596836	+	0.802363i	$0.703576\pi$
$614$	12.1945	0.492131
$615$	0	0
$616$	−15.8897	−0.640212
$617$	19.5620	0.787537	0.393769	−	0.919210i	$-0.371171\pi$
$617$	19.5620	0.787537	0.393769	+	0.919210i	$0.371171\pi$
$618$	7.65862	0.308075
$619$	4.55802	0.183202	0.0916011	−	0.995796i	$-0.470802\pi$
$619$	4.55802	0.183202	0.0916011	+	0.995796i	$0.470802\pi$
$620$	0	0
$621$	−0.669466	−0.0268648
$622$	−2.63578	−0.105685
$623$	−14.4857	−0.580357
$624$	−9.91073	−0.396747
$625$	0	0
$626$	−8.46123	−0.338179
$627$	13.9554	0.557323
$628$	−3.35432	−0.133852
$629$	−2.11702	−0.0844111
$630$	0	0
$631$	0.619092	0.0246457	0.0123228	−	0.999924i	$-0.496077\pi$
$631$	0.619092	0.0246457	0.0123228	+	0.999924i	$0.496077\pi$
$632$	38.7134	1.53994
$633$	2.58347	0.102684
$634$	7.93827	0.315269
$635$	0	0
$636$	1.11614	0.0442577
$637$	−16.9955	−0.673388
$638$	8.23702	0.326107
$639$	8.17608	0.323441
$640$	0	0
$641$	42.0848	1.66225	0.831125	−	0.556086i	$-0.187698\pi$
$641$	42.0848	1.66225	0.831125	+	0.556086i	$0.187698\pi$
$642$	3.80372	0.150121
$643$	−32.2615	−1.27227	−0.636135	−	0.771578i	$-0.719468\pi$
$643$	−32.2615	−1.27227	−0.636135	+	0.771578i	$0.719468\pi$
$644$	1.10869	0.0436885
$645$	0	0
$646$	69.0878	2.71822
$647$	−3.25289	−0.127884	−0.0639422	−	0.997954i	$-0.520367\pi$
$647$	−3.25289	−0.127884	−0.0639422	+	0.997954i	$0.520367\pi$
$648$	−2.45010	−0.0962491
$649$	−4.11065	−0.161357
$650$	0	0
$651$	11.1054	0.435255
$652$	10.2258	0.400475
$653$	−17.8165	−0.697215	−0.348607	−	0.937269i	$-0.613345\pi$
$653$	−17.8165	−0.697215	−0.348607	+	0.937269i	$0.613345\pi$
$654$	12.8751	0.503455
$655$	0	0
$656$	52.9350	2.06676
$657$	−14.1727	−0.552931
$658$	6.03662	0.235332
$659$	−35.3504	−1.37706	−0.688529	−	0.725209i	$-0.741743\pi$
$659$	−35.3504	−1.37706	−0.688529	+	0.725209i	$0.741743\pi$
$660$	0	0
$661$	−34.5543	−1.34401	−0.672003	−	0.740548i	$-0.734566\pi$
$661$	−34.5543	−1.34401	−0.672003	+	0.740548i	$0.734566\pi$
$662$	−13.4820	−0.523994
$663$	−11.2820	−0.438155
$664$	13.6591	0.530075
$665$	0	0
$666$	0.620156	0.0240306
$667$	2.11454	0.0818754
$668$	3.36509	0.130199
$669$	−0.956824	−0.0369929
$670$	0	0
$671$	20.8267	0.804005
$672$	9.21797	0.355591
$673$	22.6275	0.872226	0.436113	−	0.899892i	$-0.356355\pi$
$673$	22.6275	0.872226	0.436113	+	0.899892i	$0.356355\pi$
$674$	37.2689	1.43554
$675$	0	0
$676$	−3.63328	−0.139741
$677$	0.741784	0.0285091	0.0142545	−	0.999898i	$-0.495462\pi$
$677$	0.741784	0.0285091	0.0142545	+	0.999898i	$0.495462\pi$
$678$	−26.2731	−1.00901
$679$	−52.8651	−2.02878
$680$	0	0
$681$	−2.45535	−0.0940892
$682$	−7.47474	−0.286222
$683$	21.4927	0.822396	0.411198	−	0.911546i	$-0.365110\pi$
$683$	21.4927	0.822396	0.411198	+	0.911546i	$0.365110\pi$
$684$	−3.56362	−0.136259
$685$	0	0
$686$	6.10969	0.233269
$687$	4.34066	0.165606
$688$	−8.51584	−0.324663
$689$	5.53918	0.211026
$690$	0	0
$691$	−13.8003	−0.524987	−0.262493	−	0.964934i	$-0.584545\pi$
$691$	−13.8003	−0.524987	−0.262493	+	0.964934i	$0.584545\pi$
$692$	−9.22655	−0.350741
$693$	6.48530	0.246356
$694$	6.10120	0.231599
$695$	0	0
$696$	7.73877	0.293337
$697$	60.2590	2.28247
$698$	−39.9518	−1.51220
$699$	−5.97881	−0.226139
$700$	0	0
$701$	−31.2632	−1.18079	−0.590397	−	0.807113i	$-0.701029\pi$
$701$	−31.2632	−1.18079	−0.590397	+	0.807113i	$0.701029\pi$
$702$	3.30492	0.124736
$703$	−3.31864	−0.125165
$704$	9.43637	0.355646
$705$	0	0
$706$	16.0730	0.604915
$707$	−17.6708	−0.664577
$708$	1.04969	0.0394498
$709$	−47.2201	−1.77339	−0.886694	−	0.462358i	$-0.847004\pi$
$709$	−47.2201	−1.77339	−0.886694	+	0.462358i	$0.847004\pi$
$710$	0	0
$711$	−15.8007	−0.592574
$712$	9.16015	0.343291
$713$	−1.91886	−0.0718617
$714$	32.1063	1.20155
$715$	0	0
$716$	−2.63609	−0.0985154
$717$	22.8096	0.851841
$718$	−55.0098	−2.05295
$719$	−26.4455	−0.986252	−0.493126	−	0.869958i	$-0.664146\pi$
$719$	−26.4455	−0.986252	−0.493126	+	0.869958i	$0.664146\pi$
$720$	0	0
$721$	−19.0458	−0.709301
$722$	78.6995	2.92889
$723$	−5.79509	−0.215522
$724$	−8.72689	−0.324332
$725$	0	0
$726$	12.7731	0.474056
$727$	14.9274	0.553627	0.276813	−	0.960924i	$-0.410722\pi$
$727$	14.9274	0.553627	0.276813	+	0.960924i	$0.410722\pi$
$728$	20.1369	0.746324
$729$	1.00000	0.0370370
$730$	0	0
$731$	−9.69408	−0.358549
$732$	−5.31828	−0.196569
$733$	11.4251	0.421996	0.210998	−	0.977487i	$-0.432329\pi$
$733$	11.4251	0.421996	0.210998	+	0.977487i	$0.432329\pi$
$734$	−48.4172	−1.78711
$735$	0	0
$736$	−1.59273	−0.0587090
$737$	1.20649	0.0444416
$738$	−17.6522	−0.649785
$739$	−40.5220	−1.49063	−0.745313	−	0.666714i	$-0.767700\pi$
$739$	−40.5220	−1.49063	−0.745313	+	0.666714i	$0.767700\pi$
$740$	0	0
$741$	−17.6856	−0.649697
$742$	−15.7634	−0.578694
$743$	−3.79926	−0.139381	−0.0696907	−	0.997569i	$-0.522201\pi$
$743$	−3.79926	−0.139381	−0.0696907	+	0.997569i	$0.522201\pi$
$744$	−7.02260	−0.257461
$745$	0	0
$746$	19.0471	0.697365
$747$	−5.57490	−0.203975
$748$	−3.80510	−0.139128
$749$	−9.45924	−0.345633
$750$	0	0
$751$	31.5811	1.15241	0.576204	−	0.817306i	$-0.304533\pi$
$751$	31.5811	1.15241	0.576204	+	0.817306i	$0.304533\pi$
$752$	−4.67216	−0.170376
$753$	12.4869	0.455046
$754$	−10.4388	−0.380157
$755$	0	0
$756$	−1.65608	−0.0602310
$757$	−37.1673	−1.35087	−0.675434	−	0.737421i	$-0.736043\pi$
$757$	−37.1673	−1.35087	−0.675434	+	0.737421i	$0.736043\pi$
$758$	21.4101	0.777651
$759$	−1.12057	−0.0406740
$760$	0	0
$761$	3.90594	0.141590	0.0707951	−	0.997491i	$-0.477446\pi$
$761$	3.90594	0.141590	0.0707951	+	0.997491i	$0.477446\pi$
$762$	−29.9981	−1.08672
$763$	−32.0182	−1.15914
$764$	3.35383	0.121337
$765$	0	0
$766$	48.7288	1.76064
$767$	5.20942	0.188101
$768$	−9.82306	−0.354459
$769$	−7.68220	−0.277027	−0.138514	−	0.990361i	$-0.544232\pi$
$769$	−7.68220	−0.277027	−0.138514	+	0.990361i	$0.544232\pi$
$770$	0	0
$771$	−16.0155	−0.576784
$772$	−4.81393	−0.173257
$773$	−43.8076	−1.57565	−0.787824	−	0.615900i	$-0.788792\pi$
$773$	−43.8076	−1.57565	−0.787824	+	0.615900i	$0.788792\pi$
$774$	2.83977	0.102073
$775$	0	0
$776$	33.4297	1.20006
$777$	−1.54223	−0.0553272
$778$	−43.9131	−1.57436
$779$	94.4619	3.38445
$780$	0	0
$781$	13.6853	0.489699
$782$	−5.54751	−0.198379
$783$	−3.15855	−0.112877
$784$	−37.4338	−1.33692
$785$	0	0
$786$	12.0304	0.429109
$787$	−39.6332	−1.41277	−0.706385	−	0.707828i	$-0.749675\pi$
$787$	−39.6332	−1.41277	−0.706385	+	0.707828i	$0.749675\pi$
$788$	−2.35070	−0.0837401
$789$	−5.41400	−0.192743
$790$	0	0
$791$	65.3370	2.32312
$792$	−4.10104	−0.145724
$793$	−26.3936	−0.937265
$794$	11.5832	0.411072
$795$	0	0
$796$	6.39887	0.226802
$797$	−6.03035	−0.213606	−0.106803	−	0.994280i	$-0.534061\pi$
$797$	−6.03035	−0.213606	−0.106803	+	0.994280i	$0.534061\pi$
$798$	50.3298	1.78166
$799$	−5.31859	−0.188158
$800$	0	0
$801$	−3.73868	−0.132100
$802$	−18.1210	−0.639876
$803$	−23.7227	−0.837154
$804$	−0.308088	−0.0108654
$805$	0	0
$806$	9.47272	0.333662
$807$	−29.6868	−1.04503
$808$	11.1743	0.393109
$809$	29.2133	1.02708	0.513542	−	0.858064i	$-0.328333\pi$
$809$	29.2133	1.02708	0.513542	+	0.858064i	$0.328333\pi$
$810$	0	0
$811$	−53.5235	−1.87946	−0.939732	−	0.341912i	$-0.888926\pi$
$811$	−53.5235	−1.87946	−0.939732	+	0.341912i	$0.888926\pi$
$812$	5.23081	0.183565
$813$	4.27710	0.150004
$814$	1.03803	0.0363830
$815$	0	0
$816$	−24.8493	−0.869900
$817$	−15.1964	−0.531656
$818$	−29.3076	−1.02472
$819$	−8.21881	−0.287189
$820$	0	0
$821$	−38.2003	−1.33320	−0.666600	−	0.745415i	$-0.732251\pi$
$821$	−38.2003	−1.33320	−0.666600	+	0.745415i	$0.732251\pi$
$822$	−31.1077	−1.08501
$823$	23.1959	0.808557	0.404279	−	0.914636i	$-0.367523\pi$
$823$	23.1959	0.808557	0.404279	+	0.914636i	$0.367523\pi$
$824$	12.0437	0.419564
$825$	0	0
$826$	−14.8250	−0.515828
$827$	−38.6986	−1.34568	−0.672841	−	0.739787i	$-0.734926\pi$
$827$	−38.6986	−1.34568	−0.672841	+	0.739787i	$0.734926\pi$
$828$	0.286147	0.00994429
$829$	30.9717	1.07569	0.537846	−	0.843043i	$-0.319238\pi$
$829$	30.9717	1.07569	0.537846	+	0.843043i	$0.319238\pi$
$830$	0	0
$831$	10.0695	0.349308
$832$	−11.9587	−0.414593
$833$	−42.6131	−1.47646
$834$	−4.52752	−0.156775
$835$	0	0
$836$	−5.96487	−0.206299
$837$	2.86625	0.0990720
$838$	8.98233	0.310290
$839$	27.4310	0.947023	0.473511	−	0.880788i	$-0.342986\pi$
$839$	27.4310	0.947023	0.473511	+	0.880788i	$0.342986\pi$
$840$	0	0
$841$	−19.0236	−0.655985
$842$	−13.1561	−0.453389
$843$	−18.4511	−0.635491
$844$	−1.10424	−0.0380095
$845$	0	0
$846$	1.55802	0.0535658
$847$	−31.7648	−1.09145
$848$	12.2004	0.418964
$849$	−16.4247	−0.563695
$850$	0	0
$851$	0.266475	0.00913465
$852$	−3.49466	−0.119725
$853$	29.5779	1.01273	0.506364	−	0.862320i	$-0.330989\pi$
$853$	29.5779	1.01273	0.506364	+	0.862320i	$0.330989\pi$
$854$	75.1112	2.57025
$855$	0	0
$856$	5.98163	0.204448
$857$	49.1607	1.67930	0.839650	−	0.543129i	$-0.182760\pi$
$857$	49.1607	1.67930	0.839650	+	0.543129i	$0.182760\pi$
$858$	5.53185	0.188854
$859$	−24.9344	−0.850751	−0.425376	−	0.905017i	$-0.639858\pi$
$859$	−24.9344	−0.850751	−0.425376	+	0.905017i	$0.639858\pi$
$860$	0	0
$861$	43.8981	1.49604
$862$	34.3348	1.16945
$863$	−41.8600	−1.42493	−0.712466	−	0.701707i	$-0.752422\pi$
$863$	−41.8600	−1.42493	−0.712466	+	0.701707i	$0.752422\pi$
$864$	2.37911	0.0809390
$865$	0	0
$866$	55.3117	1.87957
$867$	−11.2874	−0.383341
$868$	−4.74673	−0.161115
$869$	−26.4476	−0.897174
$870$	0	0
$871$	−1.52898	−0.0518076
$872$	20.2470	0.685650
$873$	−13.6442	−0.461786
$874$	−8.69627	−0.294156
$875$	0	0
$876$	6.05779	0.204674
$877$	−20.4505	−0.690564	−0.345282	−	0.938499i	$-0.612217\pi$
$877$	−20.4505	−0.690564	−0.345282	+	0.938499i	$0.612217\pi$
$878$	50.0126	1.68784
$879$	−25.6582	−0.865429
$880$	0	0
$881$	36.9756	1.24574	0.622870	−	0.782325i	$-0.285967\pi$
$881$	36.9756	1.24574	0.622870	+	0.782325i	$0.285967\pi$
$882$	12.4830	0.420325
$883$	16.0136	0.538901	0.269451	−	0.963014i	$-0.413158\pi$
$883$	16.0136	0.538901	0.269451	+	0.963014i	$0.413158\pi$
$884$	4.82220	0.162188
$885$	0	0
$886$	−20.1272	−0.676185
$887$	15.1502	0.508694	0.254347	−	0.967113i	$-0.418139\pi$
$887$	15.1502	0.508694	0.254347	+	0.967113i	$0.418139\pi$
$888$	0.975242	0.0327270
$889$	74.6004	2.50202
$890$	0	0
$891$	1.67382	0.0560752
$892$	0.408971	0.0136934
$893$	−8.33742	−0.279001
$894$	19.8228	0.662974
$895$	0	0
$896$	52.4681	1.75284
$897$	1.42009	0.0474155
$898$	26.2609	0.876338
$899$	−9.05318	−0.301941
$900$	0	0
$901$	13.8885	0.462692
$902$	−29.5466	−0.983794
$903$	−7.06205	−0.235010
$904$	−41.3164	−1.37416
$905$	0	0
$906$	29.6861	0.986255
$907$	2.85565	0.0948204	0.0474102	−	0.998876i	$-0.484903\pi$
$907$	2.85565	0.0948204	0.0474102	+	0.998876i	$0.484903\pi$
$908$	1.04948	0.0348282
$909$	−4.56073	−0.151270
$910$	0	0
$911$	53.1257	1.76013	0.880067	−	0.474849i	$-0.157497\pi$
$911$	53.1257	1.76013	0.880067	+	0.474849i	$0.157497\pi$
$912$	−38.9537	−1.28989
$913$	−9.33139	−0.308824
$914$	−18.1956	−0.601856
$915$	0	0
$916$	−1.85531	−0.0613011
$917$	−29.9176	−0.987966
$918$	8.28647	0.273494
$919$	52.4797	1.73115	0.865573	−	0.500783i	$-0.166955\pi$
$919$	52.4797	1.73115	0.865573	+	0.500783i	$0.166955\pi$
$920$	0	0
$921$	−7.82693	−0.257906
$922$	21.9468	0.722780
$923$	−17.3434	−0.570864
$924$	−2.77198	−0.0911915
$925$	0	0
$926$	−11.1114	−0.365145
$927$	−4.91561	−0.161450
$928$	−7.51454	−0.246677
$929$	−14.0294	−0.460289	−0.230144	−	0.973156i	$-0.573920\pi$
$929$	−14.0294	−0.460289	−0.230144	+	0.973156i	$0.573920\pi$
$930$	0	0
$931$	−66.8003	−2.18929
$932$	2.55550	0.0837081
$933$	1.69175	0.0553854
$934$	24.3206	0.795795
$935$	0	0
$936$	5.19724	0.169877
$937$	−18.7408	−0.612235	−0.306117	−	0.951994i	$-0.599030\pi$
$937$	−18.7408	−0.612235	−0.306117	+	0.951994i	$0.599030\pi$
$938$	4.35119	0.142071
$939$	5.43076	0.177226
$940$	0	0
$941$	31.7009	1.03342	0.516710	−	0.856160i	$-0.327156\pi$
$941$	31.7009	1.03342	0.516710	+	0.856160i	$0.327156\pi$
$942$	12.2269	0.398375
$943$	−7.58497	−0.247001
$944$	11.4741	0.373450
$945$	0	0
$946$	4.75327	0.154542
$947$	−58.4999	−1.90099	−0.950496	−	0.310738i	$-0.899424\pi$
$947$	−58.4999	−1.90099	−0.950496	+	0.310738i	$0.899424\pi$
$948$	6.75364	0.219348
$949$	30.0637	0.975909
$950$	0	0
$951$	−5.09510	−0.165220
$952$	50.4896	1.63638
$953$	−24.5978	−0.796801	−0.398401	−	0.917211i	$-0.630435\pi$
$953$	−24.5978	−0.796801	−0.398401	+	0.917211i	$0.630435\pi$
$954$	−4.06846	−0.131721
$955$	0	0
$956$	−9.74942	−0.315319
$957$	−5.28685	−0.170900
$958$	2.44055	0.0788505
$959$	77.3599	2.49808
$960$	0	0
$961$	−22.7846	−0.734988
$962$	−1.31550	−0.0424133
$963$	−2.44138	−0.0786724
$964$	2.47697	0.0797778
$965$	0	0
$966$	−4.04131	−0.130027
$967$	−35.6914	−1.14776	−0.573879	−	0.818940i	$-0.694562\pi$
$967$	−35.6914	−1.14776	−0.573879	+	0.818940i	$0.694562\pi$
$968$	20.0867	0.645612
$969$	−44.3433	−1.42451
$970$	0	0
$971$	−12.5154	−0.401639	−0.200820	−	0.979628i	$-0.564360\pi$
$971$	−12.5154	−0.401639	−0.200820	+	0.979628i	$0.564360\pi$
$972$	−0.427425	−0.0137097
$973$	11.2592	0.360954
$974$	10.5383	0.337668
$975$	0	0
$976$	−58.1338	−1.86082
$977$	38.3289	1.22625	0.613126	−	0.789985i	$-0.289912\pi$
$977$	38.3289	1.22625	0.613126	+	0.789985i	$0.289912\pi$
$978$	−37.2745	−1.19191
$979$	−6.25788	−0.200003
$980$	0	0
$981$	−8.26373	−0.263841
$982$	2.01680	0.0643587
$983$	6.54478	0.208746	0.104373	−	0.994538i	$-0.466716\pi$
$983$	6.54478	0.208746	0.104373	+	0.994538i	$0.466716\pi$
$984$	−27.7593	−0.884936
$985$	0	0
$986$	−26.1732	−0.833526
$987$	−3.87455	−0.123328
$988$	7.55927	0.240493
$989$	1.22022	0.0388008
$990$	0	0
$991$	33.4437	1.06238	0.531188	−	0.847254i	$-0.321746\pi$
$991$	33.4437	1.06238	0.531188	+	0.847254i	$0.321746\pi$
$992$	6.81912	0.216507
$993$	8.65332	0.274605
$994$	49.3559	1.56547
$995$	0	0
$996$	2.38285	0.0755036
$997$	20.0965	0.636461	0.318231	−	0.948013i	$-0.396911\pi$
$997$	20.0965	0.636461	0.318231	+	0.948013i	$0.396911\pi$
$998$	8.33738	0.263915
$999$	−0.398041	−0.0125935

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3525.2.a.bg.1.8		10
5.2	odd	4		705.2.c.b.424.16	yes	20
5.3	odd	4		705.2.c.b.424.5	✓	20
5.4	even	2		3525.2.a.bf.1.3		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
705.2.c.b.424.5	✓	20	5.3	odd	4
705.2.c.b.424.16	yes	20	5.2	odd	4
3525.2.a.bf.1.3		10	5.4	even	2
3525.2.a.bg.1.8		10	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 3525 = 3 \cdot 5^{2} \cdot 47 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3525.a (trivial)

\(f(q)\)	\(=\)	\(q+1.55802 q^{2} -1.00000 q^{3} +0.427425 q^{4} -1.55802 q^{6} +3.87455 q^{7} -2.45010 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.55802 q^{2} -1.00000 q^{3} +0.427425 q^{4} -1.55802 q^{6} +3.87455 q^{7} -2.45010 q^{8} +1.00000 q^{9} +1.67382 q^{11} -0.427425 q^{12} -2.12123 q^{13} +6.03662 q^{14} -4.67216 q^{16} -5.31859 q^{17} +1.55802 q^{18} -8.33742 q^{19} -3.87455 q^{21} +2.60785 q^{22} +0.669466 q^{23} +2.45010 q^{24} -3.30492 q^{26} -1.00000 q^{27} +1.65608 q^{28} +3.15855 q^{29} -2.86625 q^{31} -2.37911 q^{32} -1.67382 q^{33} -8.28647 q^{34} +0.427425 q^{36} +0.398041 q^{37} -12.9899 q^{38} +2.12123 q^{39} -11.3299 q^{41} -6.03662 q^{42} +1.82268 q^{43} +0.715434 q^{44} +1.04304 q^{46} +1.00000 q^{47} +4.67216 q^{48} +8.01211 q^{49} +5.31859 q^{51} -0.906669 q^{52} -2.61130 q^{53} -1.55802 q^{54} -9.49303 q^{56} +8.33742 q^{57} +4.92108 q^{58} -2.45585 q^{59} +12.4426 q^{61} -4.46567 q^{62} +3.87455 q^{63} +5.63762 q^{64} -2.60785 q^{66} +0.720799 q^{67} -2.27330 q^{68} -0.669466 q^{69} +8.17608 q^{71} -2.45010 q^{72} -14.1727 q^{73} +0.620156 q^{74} -3.56362 q^{76} +6.48530 q^{77} +3.30492 q^{78} -15.8007 q^{79} +1.00000 q^{81} -17.6522 q^{82} -5.57490 q^{83} -1.65608 q^{84} +2.83977 q^{86} -3.15855 q^{87} -4.10104 q^{88} -3.73868 q^{89} -8.21881 q^{91} +0.286147 q^{92} +2.86625 q^{93} +1.55802 q^{94} +2.37911 q^{96} -13.6442 q^{97} +12.4830 q^{98} +1.67382 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 3 q^{2} - 10 q^{3} + 7 q^{4} - 3 q^{6} + 9 q^{8} + 10 q^{9}+O(q^{10}) \) 10 * q + 3 * q^2 - 10 * q^3 + 7 * q^4 - 3 * q^6 + 9 * q^8 + 10 * q^9	\( 10 q + 3 q^{2} - 10 q^{3} + 7 q^{4} - 3 q^{6} + 9 q^{8} + 10 q^{9} - 16 q^{11} - 7 q^{12} + q^{13} - 12 q^{14} - 3 q^{16} + 14 q^{17} + 3 q^{18} - 26 q^{19} + 7 q^{23} - 9 q^{24} - 10 q^{26} - 10 q^{27} - 24 q^{28} - 14 q^{29} - 22 q^{31} + 11 q^{32} + 16 q^{33} - 12 q^{34} + 7 q^{36} + 2 q^{37} - 2 q^{38} - q^{39} - 22 q^{41} + 12 q^{42} - 11 q^{43} - 36 q^{44} - 14 q^{46} + 10 q^{47} + 3 q^{48} + 2 q^{49} - 14 q^{51} + 14 q^{52} + 22 q^{53} - 3 q^{54} - 48 q^{56} + 26 q^{57} - 20 q^{58} - 37 q^{59} - 25 q^{61} - 2 q^{62} - 7 q^{64} - 4 q^{67} + 8 q^{68} - 7 q^{69} - 27 q^{71} + 9 q^{72} + q^{73} + 4 q^{74} - 42 q^{76} + 34 q^{77} + 10 q^{78} + 5 q^{79} + 10 q^{81} - 32 q^{82} + 2 q^{83} + 24 q^{84} - 6 q^{86} + 14 q^{87} - 58 q^{88} + 9 q^{89} - 64 q^{91} + 34 q^{92} + 22 q^{93} + 3 q^{94} - 11 q^{96} - 40 q^{97} + 29 q^{98} - 16 q^{99}+O(q^{100}) \) 10 * q + 3 * q^2 - 10 * q^3 + 7 * q^4 - 3 * q^6 + 9 * q^8 + 10 * q^9 - 16 * q^11 - 7 * q^12 + q^13 - 12 * q^14 - 3 * q^16 + 14 * q^17 + 3 * q^18 - 26 * q^19 + 7 * q^23 - 9 * q^24 - 10 * q^26 - 10 * q^27 - 24 * q^28 - 14 * q^29 - 22 * q^31 + 11 * q^32 + 16 * q^33 - 12 * q^34 + 7 * q^36 + 2 * q^37 - 2 * q^38 - q^39 - 22 * q^41 + 12 * q^42 - 11 * q^43 - 36 * q^44 - 14 * q^46 + 10 * q^47 + 3 * q^48 + 2 * q^49 - 14 * q^51 + 14 * q^52 + 22 * q^53 - 3 * q^54 - 48 * q^56 + 26 * q^57 - 20 * q^58 - 37 * q^59 - 25 * q^61 - 2 * q^62 - 7 * q^64 - 4 * q^67 + 8 * q^68 - 7 * q^69 - 27 * q^71 + 9 * q^72 + q^73 + 4 * q^74 - 42 * q^76 + 34 * q^77 + 10 * q^78 + 5 * q^79 + 10 * q^81 - 32 * q^82 + 2 * q^83 + 24 * q^84 - 6 * q^86 + 14 * q^87 - 58 * q^88 + 9 * q^89 - 64 * q^91 + 34 * q^92 + 22 * q^93 + 3 * q^94 - 11 * q^96 - 40 * q^97 + 29 * q^98 - 16 * q^99

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